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Expert Systems with Applications 39 (2012) 7763–7775 Contents lists available at SciVerse ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa Analyzing the solutions of DEA through information visualization and data mining techniques: SmartDEA framework Alp Eren Akçay a,1, Gürdal Ertek a,⇑, Gülçin Büyüközkan b a b Sabancı University, Faculty of Engineering and Natural Sciences, Orhanli, Tuzla, 34956 Istanbul, Turkey ~an Cad No: 36, 34257 Ortaköy, Istanbul, Turkey Department of Industrial Engineering, Galatasaray University, Çırag a r t i c l e i n f o Keywords: Data envelopment analysis (DEA) Information visualization Data mining Decision support system framework a b s t r a c t Data envelopment analysis (DEA) has proven to be a useful tool for assessing efﬁciency or productivity of organizations, which is of vital practical importance in managerial decision making. DEA provides a significant amount of information from which analysts and managers derive insights and guidelines to promote their existing performances. Regarding to this fact, effective and methodologic analysis and interpretation of DEA results are very critical. The main objective of this study is then to develop a general decision support system (DSS) framework to analyze the results of basic DEA models. The paper formally shows how the results of DEA models should be structured so that these solutions can be examined and interpreted by analysts through information visualization and data mining techniques effectively. An innovative and convenient DEA solver, SmartDEA, is designed and developed in accordance with the proposed analysis framework. The developed software provides DEA results which are consistent with the framework and are ready-to-analyze with data mining tools, thanks to their specially designed table-based structures. The developed framework is tested and applied in a real world project for benchmarking the vendors of a leading Turkish automotive company. The results show the effectiveness and the efﬁcacy of the proposed framework. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Data envelopment analysis (DEA) is a widely used method in performance evaluation and benchmarking of a set of entities. The popularity of DEA can be easily conﬁrmed in the article of Emrouznejad, Parker, and Tavares (2008) that has summarized previous DEA contributions during the past three decades. Its convenience in assessing the multiple input and output variables of these entities by not requiring congruity and an apriori relationship makes it a very popular management tool in many application areas. Another reason for its wide use is the managerial insights that come up with the solution of a DEA model. For instance, DEA assigns a peer group or reference set for an inefﬁcient entity. The entity can take the entities in this reference set as role models in accordance with the assigned weights. Another important DEA result is the target values or projections for the input and output variables of an inefﬁcient entity to achieve full efﬁciency. DEA thus provides signiﬁcant amount of information from which analysts and managers derive insights and guidelines to enhance their existing performances. Regarding to this fact, effective and ⇑ Corresponding author. Tel.: +90 216 483 9568; fax: +90 216 483 9550. E-mail address: ertekg@sabanciuniv.edu (G. Ertek). Present address: Carnegie Mellon University, Tepper School of Business, 5000 Forbes Avenue, Pittsburgh, 15213 PA, USA. 1 0957-4174/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2012.01.059 methodologic analysis and interpretation of DEA solutions is very critical (El-Mahgary & Lahdelma, 1995; Emrouznejad & De Witte, 2010; Yadav, Padhy, & Gupta, 2010). The main contribution in this study is the development of a general framework that enables DEA analysts to extract the most important and interesting insights in a systematic manner. In order to do so, a computer science and data mining perspective is adopted for designing the structure of the DEA results. Various data mining and information visualization techniques can be appropriate for the analysis of different types of DEA models (Lin, Lin, Li, & Kuo, 2008; Seol, Lee, & Kim, 2011). The paper provides a fundamental basis for the implementation of these techniques in the DEA solutions. A convenient and general notation is proposed for the DEA data included in the model, the other data and the results data generated by DEA solvers. The ultimate goal of the study is then to build a structure framework for the analysis of DEA results, enabling researchers and practitioners to make analytical benchmarking and performance evaluations. In accordance with the proposed framework, a user-friendly and convenient DEA software, SmartDEA, is designed and developed. The software generates DEA solutions with a structure consistent with the framework. The analysis steps performed by a DEA analyst are importing the model data, analyzing the data by solving the appropriate DEA model, and making analytical inquires on the generated solution data to evaluate and benchmark 7764 A.E. Akçay et al. / Expert Systems with Applications 39 (2012) 7763–7775 the entities assessed in DEA model. The solution data generated by the software allows analysts to integrate the results and many of the data mining and information visualization techniques in a convenient and effective manner. The rest of this paper is organized as follows: after a brief introduction to the DEA, the theory of the basic DEA models are explained in Section 2, providing a fundamental background for DEA. Since it is critical to know when and where DEA is an appropriate method, advantages and drawbacks of DEA are also explained in the same section. Proposed framework, which is based on the integration of DEA results with data mining and information visualization techniques, is presented in Section 3. An overview of existing DEA software is followed by the presentation of the developed DEA solver, SmartDEA, in Section 4. The testing of the framework and SmartDEA with the real world data of an automotive company is illustrated in Section 5. Concluding remarks are summarized in Section 6. composite unit (i.e. virtual producer – with respect to which the efﬁciency score of the inefﬁcient DMU is found) are also computed by the DEA model. One important shortcoming of DEA is the rank ordering of the efﬁciency scores for each DMU. Each inefﬁcient DMU is labeled as such only in comparison to the given group, and this may be misleading: An inefﬁcient DMU may have been labeled as efﬁcient if it were part of an inferior group. Conversely, an efﬁcient DMU may not necessarily be efﬁcient when compared as a part of another group. Also, theoretically, only the DMUs with the same reference sets can be strictly rank ordered (Avkıran, 1999). Yet another important result DEA provides is the target inputs and target outputs, which are referred to as projections. They represent up to which value an input should be decreased while keeping the outputs at the same levels (i.e. input orientation) or how much an output should be increased while the input level remains unincreased (i.e. output orientation), respectively, so that the DMU becomes efﬁcient. 2. Data envelopment analysis (DEA) 2.2. Basic DEA models 2.1. Introduction to the DEA Since its introduction by Charnes et al. (1978) in their seminal work measuring efﬁciency of decision making units, the CCR model served as the origin of many following ideas and models in DEA literature. Cooper et al. (2006) discusses the model in detail together with the classical alternative models. The theoretical formulations and summaries in this section are based on Cooper et al. (2006). Let’s suppose that there are n DMUs in the model: DMU1, DMU2 , . . . , DMUn. Suppose there are m inputs and s outputs for each one of them. For DMUj the inputs and outputs are represented by (x1j, x2j, xmj) and (y1j, y2j, ysj), respectively. As stated previously, for each DMUo, DEA tries to maximize the ratio DEA is a nonparametric performance evaluation technique with a wide range of application areas within various disciplines. In their breakthrough study, Charnes, Cooper, and Rhodes (1978) deﬁne DEA as ‘‘a mathematical programming model applied to observational data and a new way of obtaining empirical estimates of relations such as the production functions and/or efﬁcient production possibility surfaces’’. Since its introduction in 1978, researchers in a multitude of disciplines distinguished and adopted DEA as a promising tool that is easily applicable to their ﬁelds for performance evaluation and benchmarking of entities and operational processes. A given set of entities, referred to as decision making units (DMU) in DEA terminology, can be conveniently compared in terms of multiple inputs and multiple outputs, assuming neither a speciﬁc form of relationship between inputs and outputs, nor ﬁxed weights for the inputs and outputs of a DMU. DEA ﬁrstly provides an efﬁciency score between 0 and 1 for each DMU involved in the analysis. The efﬁciency score for a DMU is determined by computing the ratio of total weighted outputs to total weighted inputs for it. DEA enables variable weights, which are calculated in such a way that the efﬁciency score for the DMU is maximized (Cooper, Seiford, & Tone, 2006). For a DEA model with n different DMUs, n different linear programming (LP) optimization models are solved to compute the efﬁciency scores of each of the DMUs. A basic DEA model can provide important metrics and benchmarks for monitoring the comparative performances of entities in a group and take managerial actions to improve them. An efﬁcient frontier or envelopment surface, which is drawn over the ‘‘best’’ DMUs, is the critical component of a DEA model. It is formed by the efﬁcient DMUs which have efﬁciency scores of 1. The efﬁciency score of a DMU is basically the distance from each DMU to this efﬁcient frontier. The efﬁciency scores of the inefﬁcient DMUs are calculated in accordance with this distance represented as a Pareto ratio. Besides the efﬁciency scores, another result offered by DEA is the reference sets, or peer (sub) groups. For each inefﬁcient unit, DEA identiﬁes a set of corresponding efﬁcient units that can serve as a benchmark peer group for the selected DMU. The solution of the LP formulation of the model results in the reference set for each DMU. Knowing that the DMUs in the reference set are efﬁcient and have the same input and output structure, they can be regarded as ‘‘good’’ examples operating practices for the corresponding inefﬁcient DMU (Boussoﬁane, Dyson, & Thanassoulis, 1991). The percentages of each reference set unit contributing to the Virtual output Virtual input ð1Þ where Virtual input ¼ v 1 x1o þ þ v m xmo ð2Þ Virtual output ¼ u1 y1o þ þ us yso ð3Þ and the weights vi and ur are not ﬁxed in advance. Best weights are assigned according to the solution of the following fractional DEA model (M1): ðFPo Þ max s:t: h¼ u1 y1o þ þ us yso v 1 x1o þ þ v m xmo u1 y1o þ þ us yso v 1 x1o þ . . . þ v m xmo v 1; v 2; . . . ; v m P 0 61 u1 ; u2 ; . . . ; us P 0 The fractional model can be transformed into the linear model shown below (M2): ðLPo Þ max s:t: h ¼ u1 y1o þ þ us yso v 1 x1o þ þ v m xmo ¼ 1 u1 y1j þ þ us ysj 6 v 1 x1j þ þ v m xmj v 1; v 2; . . . ; v m P 0 u1 ; u2 ; . . . ; us P 0 The fractional model (M1) is equivalent to linear model (M2), and Unit Invariance Theorem states that the optimal values of max h = h⁄ in M1 and M2 are independent of the units in which the inputs and outputs are measured, under the requirement that these units are the same for every DMU. The input and output data can be arranged in matrix notation X and Y, respectively: